Won't be the starter......

But that fuel pump shounds like its shot to me, either that or you have a blocked line someplace.

Now in 1962 you might want to check that fuel pump and see if it has a filter on the bottom of it, it just unscrews (use a small filter type wrench) and you replace the filter, those often just get clogged. Either that or be checking for an in-line filter somplace.

Reminds me of a great story and a learned lesson.

I had a 70 pontiac once that I had gotten for free, because it did not run, it had a 455, replaced the fuel pump (after I had diagnosed it to that), run great for two weeks, then same deal, replaced the pump again and it again ran for two weeks, did htis four times and got tireds so I bought a brand new pump (rather than a rebuilt), with the new pump it only ran 4 days. Each time it stranded me in different places, I was so sick of that car.
So I parted it out.

As I was parting it out, sold the gas tank only to find a mouse nest inside of it, evidently before I had gotten it when the car had been sitting some mouse (or a family) had made a very nice home inside the gas tank complete with leaves. When I got it I disrupted the happy family and completely washed out the "house" with gas when I filled the tank.
Evidently every so often the tank level and the suction from the pump would cause the leaves or a family member to restrict the gas line enough to cause the engine to starve for fuel and/or the pump to destroy itself (since I had checked a couple of them).

Learned my lesson there. Now any car that does not have a gas cap gets the tank removed and flushed.

Bill White
White Automotive